The investment is led by Brazilian group OutField, an international consortium co-founded by Pedro Olivera, and includes Georgios Frangulis, CEO of global health-food brand OakBerry.
"Djokovic, the most successful player in history, whose mental strength and unique approach will bring considerable added value," the club said in a statement.
"Massa (15 seasons in Formula 1) and Magnussen (10 seasons), who will help create a bridge between football and motorsport – a distinctive strength of the Le Mans brand."
Le Mans begin their Ligue 2 campaign on 9 August away at Guingamp.